Zero-sequence parameter measurement and ground voltage control method for resonant ground system based on virtual ground principle

ABSTRACT

The present disclosure provides a zero-sequence parameter measurement and ground voltage control method for a resonant ground system based on a virtual ground principle. The method, based on the virtual ground principle, arbitrarily specifies a point K in a phasor plane in which three-phase voltages are located. A virtual ground control method is used to achieve virtual ground of the point K, and an accurate zero-sequence resonant parameter of a zero-sequence network under an action of the excitation {dot over (U)} KN  can be obtained. When a single-phase ground fault occurs, a ground phase is specified as a target working point, and a control method is applied to cause the zero-sequence network to accurately resonate, and a voltage of this phase relative to ground is 0. At this time, both a residual voltage and a residual current of the fault phase are effectively suppressed.

TECHNICAL FIELD

The present disclosure relates to a zero-sequence parameter measurementand ground voltage control method for a resonant ground system based ona virtual ground principle, and in particular, to an on-line accuratemeasurement method for zero-sequence parameters of a resonant groundsystem and a method for controlling a voltage of a single-phase groundincluding virtual ground) fault relative to ground, which can achieveeffect of high-precision measurement and low residual voltage control,and the virtual ground principle is universal.

BACKGROUND

The key to a resonant ground system lies in that a reactance currentflowing through a neutral point must be exactly equal to a distributedcapacitive current of the three-phase relative to ground, such that thearc-suppression reactance and the line distributed capacitance are inparallel resonance to achieve the lowest fault phase-to-ground voltage,which is 0 volts theoretically. Being affected by changes in operatingconditions of a power distribution network, the line distributedcapacitance and conductance parameters usually change, and it isdifficult to measure accurately, so it is impossible to accurately setparameters of an arc-suppression reactor in advance. For arc-suppressiondevices such as a preadjusted turn reactance, a preset parameterphase-controlled reactance, a preset parameter capacity and tuneregulating reactance, etc., there are precision problems of presetparameters, i.e., the measurement deviation of a zero-sequencecapacitance causes an actual working point to shift. However, the activeconsumption caused by line conductance, coil internal resistance, groundresistance, etc., will result in greater control deviation, which cannotbe compensated by the arc-suppression reactance. Therefore, after thearc-suppression device operates, there is always a certain residualvoltage and a ground residual current at the fault phase ground pointrelative to the ground.

The existing control scheme inherits characteristics of the LC resonanceof the zero-sequence circuit, and develops in several aspects such asaccurate measurement about the zero-sequence parameters, accurateadjustment of the arc-suppression reactance, accurate measurement andcompensation of an active component, etc. However, these aspects arebasically implemented separately, and in particular, there is a lack ofeffective correlation between measurement behavior and arc-suppressionbehavior, with the former being not accurate and the latter being not inplace. Thus, a perfect solution, which integrates and broadens theexisting theory, establishes an integrated arc-suppression system formeasurement and control, effectively solves the problem of activecomponent compensation, accurate resonance and residual voltage residualcurrent limitation in an arc-suppression state, is still needed.

SUMMARY

The object of the present disclosure is to provide a zero-sequenceparameter measurement and ground voltage control method for a resonantground system based on a virtual ground principle, in view of thedeficiencies of the related art.

The present disclosure proposes: arbitrarily specifying a point K in aphasor plane in which three-phase voltages are located, a voltagerelative to a neutral point N being {dot over (U)}_(KN), using a groundpoint voltage zeroing control scheme, the zero-sequence network beingthe accurate resonance under an action of {dot over (U)}_(KN), causing avoltage of the specified point K relative to ground to be 0, i.e.,equivalent to that the point K being grounded, which is here namedvirtual ground. In particular, if the specified point K coincides with aline voltage phasor of any phase, this phase is grounded, which isequivalent to the fault ground condition in an existing system. Thevirtual ground method does not require the point K to apply a transitionimpedance to ground, and does not even need to be physically visible,and is valid for the entire phasor plane.

i) According to the virtual ground principle, when an effective valueand a phase of the voltage {dot over (U)}_(KN) of the specified point Kare exact values, virtual ground is achieved, and accurate zero-orderresonant parameters of the zero-sequence network under an action of theexcitation source {dot over (U)}_(KN) can be obtained. During themeasurement, the neutral point compensation current is proportional to{dot over (U)}_(KN). If the zero-sequence parameters have sufficientmeasurement precision and have no effect on system insulation under theapplied {dot over (U)}_(KN) excitation amplitude, it can be used as anappropriate online measurement method for zero-sequence parameters. Theobtained parameters are the zero-sequence network parameters of thepower distribution network after being equivalent according to thepositive and negative zero, and the actual symmetry of the powerdistribution network is no longer considered.

ii) When the fault phase is grounded, the ground phase voltage can bespecified as the target working point, and a virtual ground control isapplied as described above to cause the zero-sequence network toaccurately resonate, and the voltage of this phase relative to ground iszero. At this time, both the residual voltage and the residual currentof the fault phase are effectively suppressed. The accurate measurementresults in i) can be used for the pre-tuning control of thearc-suppression reactance, and the virtual ground can be used for theaccurate compensation of the inductive current difference, which canreduce the controlled source capacity and save the overall cost of thedevice. For the cost increase, the virtual ground controlled-source withfull compensation capability is provided, and online measurement andarc-suppression reactance pre-tuning control are not required.

iii) Effectively selecting the virtual ground point can achieves anincrease of the specified phase-to-ground voltage, for probing thisphase insulation while the insulation of the other two phases relativeto ground are not affected.

iv) Specifying a voltage of a small magnitude near the neutral point Nas a virtual ground clamping can effectively suppress the excitedoscillation of the line voltage.

Specifically, the virtual ground control method of the presentdisclosure is as follows:

using a conventional resonant ground manner, the neutral point N beinggrounded via a series branch of an arc-suppression inductance L, anequivalent resistance R and a controllable inverter source unit {dotover (U)}_(x), an injection current of the branch being İ_(x); taking afraction L₀/m of a standard arc-suppression reactance L₀ as an injectionbranch reactance L, and L₀,C₀ satisfying a resonant condition:

ω² L ₀ C ₀=1

then:

${\overset{.}{U}}_{x} = {{\left( {1 - \frac{1}{m}} \right){\overset{.}{U}}_{KN}} + {j\; \omega \; C_{0}R{\overset{.}{U}}_{KN}} + {\left( {R + {j\; \omega \; L}} \right)Y_{0}{\overset{.}{U}}_{KN}}}$

wherein {dot over (U)}_(KN) is a voltage of the specified point Krelative to the neutral point N, C₀ is a total zero-sequence capacitanceand is a sum of a distributed capacitance of the three phases, Y₀ is atotal zero-sequence conductance and is a sum of a distributedconductance of the three phases, ω is a power frequency angularfrequency of a power distribution network; and

taking a virtual working point K-to-ground voltage {dot over (U)}_(KG)as an input and taking a ground-to-neutral point N voltage {dot over(U)}_(GN) and a voltage drop of the system zero-sequence network currenton the injection branch as corrections to construct a negative feedbackcontrol loop, taking an appropriate complex phasor proportional integralparameter cPI[K_(p)+K_(i)/s], causing the zero-sequence circuit to enterinto an LC parallel resonant state, and the loop circuit input U_(KG)converging to 0, PI control calculation being applied to both a realpart and an imaginary part of the input complex phasor, a governingequation being as follows:

{dot over (U)} _({tilde over (x)})={dot over (U)} _(GN)+(R+jωL)(İ _(C0)İ _(Y0))+cPI[{dot over (U)} _(KG)(R+jωL)/R_(k)]

wherein the complex phasor proportional integral part is:

cPI[a+jb]=a(Kp+Ki/s)+jb(Kp+Ki/s)

R_(K) is a virtual working point-to-ground transition resistance, andİ_(C0)+İ_(Y0) is a line zero-sequence total current and is a complexconstant under a resonance convergence condition.

In the above aspect, two parameters of the line zero-sequence totalcurrent İ_(C0)+İ_(Y0) and the impedance R_(k) are ignored, and thegoverning equation is simplified as:

{dot over (U)} _({tilde over (x)}) =cPI[{dot over (U)} _(KG)]

In the method of the present disclosure, when the controlled voltagesource is injected into the neutral point of the system via thereactance, the injection can be performed in a direct-hanging mode,i.e., a compensation inductive current is injected directly into theneutral point, or a compensation current is injected into the neutralpoint by using an isolation transformer.

A phase plane is formed by the three-phase voltages {dot over (U)}_(a),{dot over (U)}_(b), {dot over (U)}_(c), and one phasor circle ABC isformed by three voltage phasors, and a selection principle of the pointK is as follows:

1) when considering device insulation, selecting an arbitrary point inthe phase plane formed by the three-phase voltages {dot over (U)}_(a),{dot over (U)}_(b), {dot over (U)}_(c) as the point K;

2) when performing zero-sequence parameter measurement, selecting aphasor circle in the phase plane with an effective value of the measuredvoltage being a radius, and point K being limited on the phasor circle;

3) when considering insulation safety, if an effective value of eachphase-to-ground voltage does not exceed √{square root over (3)}U_(φ),forming a circular arc having a radius with an effective value of√{square root over (3)}U_(φ) by taking A, B, and C as a centerrespectively, three circular arcs closing an area, selecting the workingpoint K in this area;

4) considering the phase-to-ground safety voltage, if it is supposedthat the phase B-to-ground insulation is damaged but a faulty runningtime still needs to be extended, selecting the target working point K inthe area of 3) and near the point B and appropriately reducing awithstand voltage of phase B relative to ground according to an actualinsulation tolerance.

The present disclosure applies a control method based on the virtualground principle to achieve virtual ground of the point K, and anaccurate zero-sequence resonant parameter of a zero-sequence networkunder an action of the excitation {dot over (U)}_(KN) can be obtained.When the fault phase is grounded, the specified ground phase is thetarget working point, and the voltage of this phase relative to groundis 0, so that both the residual voltage and the residual current of thefault phase are effectively suppressed. The accurate measurement schemecan be used for the pre-tuning control of the arc-suppression reactance,and the virtual ground control can be used for the accurate compensationof the inductive current difference, which can reduce the controlledsource capacity and save the overall cost of the device. For the virtualground control devices with full compensation capability, onlinemeasurement and partial reactance pre-tuning control are not required.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram of a three-phase distribution system and avirtual ground;

FIG. 2 is an equivalent zero-sequence circuit of a three-phase circuitshown in FIG. 1;

FIG. 3 is an equivalent circuit of the zero-sequence circuit shown inFIG. 2;

FIG. 4 is a negative feedback control loop;

FIG. 5 is a simplified control block diagram of the present disclosure;

FIG. 6 illustrates a simulated fault branch current curve using a systemof 10 kV and. a compensation current of 150 A;

FIG. 7 illustrates details of a convergence process;

FIG. 8 is a control scheme when a partial inductive current is suppliedby using an existing arc-suppression coil X1;

FIG. 9 is a schematic diagram of a selection range of a virtual groundworking point.

DESCRIPTION OF EMBODIMENTS

The contents of the present disclosure are explained step by step below:

1) Virtual Ground Principle

As shown in FIG. 1, a neutral point N of a main transformer (or azigzag-shaped ground transformer) is grounded via a series branch of anarc-suppression inductance L, an equivalent resistance R and acontrollable inverter source unit {dot over (U)}_(x), and the equivalentresistance R is a sum of a coil resistance r and a ground resistance Rg.The bus-to-ground voltages {dot over (U)}_(AG), {dot over (U)}_(BG) and{dot over (U)}_(CG) of three phases are measured by three voltagesensors V1, V2, and V3, respectively, and the analysis parameters andtheir reference directions are as shown in FIG. 1. The line-to-grounddistributed capacitance of the three phases are C₁, C₂ and C₃,respectively, and the conductance-to-ground are Y₁, Y₂ and Y₃,respectively. Then:

İ _(a) =İ _(C1) +İ _(Y1)=({dot over (U)} _(a) −{dot over (U)} _(GN))(jωC ₁ +Y ₁)   (1);

İ _(b) =İ _(C2) +İ _(Y2)=({dot over (U)} _(b) −{dot over (U)} _(GN))(jωC ₂ +Y ₂)   (2);

İ _(C) =İ _(C3) +İ _(Y3)=({dot over (U)} _(C) −{dot over (U)} _(GN))(jωC ₃ +Y ₃)   (3);

İ _(x)=−(İ _(a) +İ _(b) +İ _(C))   (4).

Under symmetrical conditions, the parameters of the three phasesrelative to ground are balanced, and the capacitance of each phase isC_(φ) and the conductance is Y_(φ). Moreover, the power supplies of thethree phases are also completely symmetrical. When an injection sourceU_(x) is 0, a neutral point-to-ground voltage U_(GN) is 0, and a currentI_(x) is 0.

Provided that there is an arbitrary point K on a {dot over (U)}_(abc)phasor plane, and the voltage relative to point N is {dot over(U)}_(KN). If there is an NKG fault branch in FIG. 1 and there is aground transition resistance R_(k), then:

İ _(k)=({dot over (U)} _(KN) −{dot over (U)} _(GN))/R _(k) ={dot over(U)} _(KG) R _(k)   (5).

Equation (5) is a virtual ground equation. In fact, the fault branchdoes not exist, and R_(k) is infinite, i.e., open circuit, so that thefault current remains 0.

Equations (2), (3), and (5) are substituted into equation (4), and thephase distributed capacitance C_(φ) and the distributed conductanceY_(φ) are substituted, then:

İ _(x)=−({dot over (U)} _(a) +{dot over (U)} _(b) +{dot over (U)}^(c))(jωC _(φ) +Y _(φ))+3{dot over (U)} _(GN)(jωC _(φ) +Y _(φ))−{dotover (U)} _(KG) /R _(k)   (6),

i.e.,

İ _(x) {dot over (U)} _(GN)(jω3C _(φ)+3Y _(φ))−{dot over (U)} _(XG) R_(k)   (7).

According to the Equation (7), the three-phase circuit shown in FIG. 1can be equivalent to the zero-sequence circuit shown in FIG. 2, in whichthe total zero-sequence capacitance C₀ is the sum of the distributedcapacitance C₁, C₂, C₃, of the three phases, i.e., 3C_(φ), and the totalzero-sequence conductance Y₀ is the sum of the distributed conductanceY₁, Y₂, Y₃, of the three phases, i.e., 3Y_(φ).

Considering that the point K-to-ground voltage cannot be measured, thefault phase-to-ground voltage {dot over (U)}_(KG) is obtained by thefollowing calculation:

{dot over (U)} _(KG) ={dot over (U)} _(KN) +{dot over (U)} _(NG)   (8),

where {dot over (U)}_(KN) is the set voltage of the virtual workingpoint K, and {dot over (U)}_(NG) is the neutral point-to-ground voltage.

Control is applied to the zero-sequence circuit shown in FIG. 2, suchthat the terminal voltage {dot over (U)}_(GN) of the controlledarc-suppression ground branch is exactly equal to the voltage {dot over(U)}_(KN) of the virtual working point K. The condition that the faultground branch current I_(k) is 0 can be satisfied, and R_(k) is open,and the point K-to-ground voltage {dot over (U)}_(KG) is 0. Then, thezero-sequence circuit can also be equivalent to the simple circuit shownin FIG. 3. At this time, Equation (7) is:

İ _(x) ={dot over (U)} _(KN)(jω3C _(φ)+3Y _(φ))   (9).

The injection current İ_(x) of the neutral point-controlled injectionbranch is:

İ _(x)=({dot over (U)} _(x) −{dot over (U)} _(KN))/(R+jωL)   (10).

It can be obtained from Equation (9) and Equation (10) that:

{dot over (U)} _(x)=[1+(R+jωL)(jωC ₀ +Y ₀)]{dot over (U)} _(KN)   (11).

The fraction L₀/m of the standard arc-suppression reactance L₀ is takenas the injection branch reactance L, and L₀, C₀ meet the resonantcondition:

ω² L ₀ C ₀=1   (12).

The fractional reactance value and the resonant condition aresubstituted into equation (11), then:

$\begin{matrix}{{\overset{.}{U}}_{x} = {{\left( {1 - \frac{1}{m}} \right){\overset{.}{U}}_{KN}} + {j\; \omega \; C_{0}R{\overset{.}{U}}_{KN}} + {\left( {R + {j\; \omega \; L}} \right)Y_{0}{{\overset{.}{U}}_{KN}.}}}} & (13)\end{matrix}$

Equation (13) is the controlled condition of the equivalent idealreactance in the zero-sequence circuit and can be divided into threeterms: the last term is a negative conductance voltage component forcancelling the line distributed conductance Y₀; the middle term is anegative resistance voltage component for canceling the total resistanceR of the arc-suppression injection branch; the first term is theequivalent voltage component of the partial reactance to the fullreactance. Moreover, when injecting the three-phase distribution systemshown in FIG. 1, the equivalent reactance value is continuouslyadjustable between capacitive and inductive. Equation (13) satisfies theresonant condition when and only when the residual voltage is 0.

If the line conductance is 0, the last term is 0; if the totalresistance of the injection branch R is 0, the middle tern is 0; if thefull reactance is taken and m is 1, the first term is 0. When the threeconditions are satisfied at the same time, the controlled source {dotover (U)}_(x) takes a value of 0, and the zero-sequence circuitdegenerates into a pure inductance and capacitance circuit.

When the conventional resonant ground system is single-phase grounded,the zero-sequence circuit is induced with the LC oscillation by thefault resistance R_(K) under excitation of the fault phase voltage, andthe oscillation terminal voltage converges to the fault phase voltage;under the virtual ground condition, the zero-sequence circuit is inducedwith the LC oscillation by the injection branch, and the terminalvoltage is the virtual working point voltage {dot over (U)}_(KN).

In the actual project, usually none of these three conditions issatisfied, but as long as values of the effective value and phase of thecontrolled source {dot over (U)}_(x) are taken in accordance withEquation (13), the three-phase circuit shown in FIG. 1 can obtainaccurate resonant conditions such that the residual voltage of thevirtual ground point K-to-ground is 0. Similarly, if there is such acontrol method that the residual voltage of the virtual ground pointK-to-ground is 0, then the controlled source {dot over (U)}_(x) mustsatisfy the condition of Equation (13), and the circuit is in anaccurate resonant state.

It can be obtained from Equation (7) that:

İ _(x)=({dot over (U)} _(x) −{dot over (U)} _(GN))/(R+jωL)={dot over(U)} _(GN)(jωC ₀ +Y ₀)−({dot over (U)} _(KN) −{dot over (U)} _(GN))/R_(k)   (14)

{dot over (U)} _(x) ={dot over (U)} _(GN)+(R+jωL)(jωC ₀ +Y ₀){dot over(U)} _(GN) −{dot over (U)} _(KG)(R+jωL)/R _(k)   (15)

{dot over (U)} _(x) ={dot over (U)} _(GN)−(R+jωL)(İ _(C0) +İ _(Y0))−{dotover (U)} _(KG)(R+jωL)/R _(k)   (16),

where each parameter takes the reference direction shown in FIG. 2.

According to the Equation (16), the present disclosure proposes thefollowing scheme: taking the virtual working point-to-ground voltage{dot over (U)}_(KG) as an input and taking the ground-to-neutral pointvoltage {dot over (U)}_(GN) and the voltage drop of the systemzero-sequence network current on the injection branch as corrections toconstruct a negative feedback control loop as shown in FIG. 4, takingthe appropriate complex phasor proportional integral parametercPI[K_(p)+K_(i)/s] so as to cause the zero-sequence circuit to enterinto an LC parallel resonant state, the loop circuit input U_(KG)converging to 0, and the fault branch current I_(k) being also zero. Inaddition, PI control calculation is applied to both the real part andthe imaginary part of the input complex phasor. The governing equationis as follows:

{dot over (U)} _({tilde over (x)}) ={dot over (U)} _(GN)+(R+jωL)(İ _(C0)+I _(Y0))+cPI[{dot over (U)} _(KG)(R+jωL)/R _(k)]  (17),

where the complex phasor proportional integral term is:

cPI[a+jb]=a(Kp+Ki/s)+jb(Kp+Ki/s)   (18).

In Equation (17), the line zero-sequence total current İ_(C0)+İ_(Y0) isa complex constant under the condition of resonance convergence, and themeasured value is affected by the convergence process of the groundvoltage {dot over (U)}_(KG). If the ground voltage {dot over (U)}_(KG)reliably converges, this term can take the complex constant with adeviation, or even be ignored, and be compensated by the cPI part; the{dot over (U)}_(GN) term belongs to a complex constant which has abounded amplitude and converges to the set voltage {dot over (U)}_(KN),and it can also be ignored and compensated by the cPI part. Therefore,it is indicated by a broken line in FIG. 4 and can be partially orcompletely cancelled.

In Equation (17), the impedance ratio (R+jωL)/R_(k) of the injectionbranch to the fault ground branch includes an unknown impedance R_(k),which will cause the cPI gain to change in the case of an actual groundfault, and it is open circuit and can be set to a constant in the caseof virtual ground. Thus, a simple governing expression (19) can beobtained:

{dot over (U)} _({tilde over (x)}) =cPI[{dot over (U)} _(KG)]  (19)

From the control Equation (19), the simplest control block diagram shownin FIG. 5 can be constructed.

The stability of the control system is examined by Equations (15) and(19) with R_(k) being open;

[1+(R+jωL)(jωC ₀ +Y ₀)]({dot over (U)} _(KN) −{dot over (U)}_(KG))−cPI[{dot over (U)} _(KG)]=0   (20)

its s-domain equation is:

$\begin{matrix}{{{\left\lbrack {1 + {\left( {R + {sL}} \right)\left( {{sC}_{0} + Y_{0}} \right)}} \right\rbrack \left( {{\overset{.}{U}}_{XN} - {\overset{.}{U}}_{XG}} \right)} - {\left( {K_{p} + \frac{K_{i}}{s}} \right){\overset{.}{U}}_{KG}}} = 0} & (21) \\{{\overset{.}{U}}_{KG} = {\frac{s\left\lbrack {1 + {\left( {R + {sL}} \right)\left( {{sC}_{0} + Y_{0}} \right)}} \right\rbrack}{{s^{3}{LC}_{0}} + {s^{2}\left( {{LY}_{0} + {RC}_{0}} \right)} + {s\left( {{RY}_{0} + 1 + K_{p}} \right)} + K_{i}}{\overset{.}{U}}_{KN}}} & (22)\end{matrix}$

The characteristic equation of the control system is:

s ³ LC ₀ +s ²(RC ₀ +LY ₀)+s(RY ₀+1+K _(p))+K _(i)=0   (23)

A resonant ground system having an actual capacity of 150 A isconsidered: approximately taking 3 phase-to-ground capacitors of 28 μF,with C₀ being 84 μF; taking a resonant connection inductance L as 15 mH;taking Y₀ as 3 times of single-phase conductance of 1 μS, i.e., 3 μS;taking R as 4Ω; taking R_(K) as 1Ω, which does not work in the case ofvirtual ground.

From the actual parameter analysis, the characteristic equation (23) hasthree roots: −12.53+j0, −127.09±j1252.19, all of which stably converge.

2) Simulation Verification of Single Point Virtual Ground ConvergenceBased on a Virtual Ground Control Method

A simulation system is constructed based on the above system parameters,and one voltage phasor {dot over (U)}_(KN) is arbitrarily specified, and{dot over (U)}_(KG) reliably converges to 0. The specified voltagephasor can be independent of the tolerance of the system insulation anda fault branch is not required.

3) Simulation Verification of Zero-Sequence Parameter Measurement Basedon Virtual Ground Control Method

The voltage phasor {dot over (U)}_(KN) is set to 100+j0(V), and avirtual ground control is applied, such that {dot over (U)}_(KG)reliably converges to 0, and the measured injection current is0.0419+j2.6385(A). Namely, when the LC resonant terminal voltage of thezero-sequence circuit is 100V, the injection capacitive currentcomponent is 2.6385 A, the corresponding zero-sequence capacitance valueis 83.986 μF, the set value is 84 μF, and the deviation is −0.166‰. Whensimulating with different zero-sequence parameters and controlparameters, the calculated values of the zero-sequence capacitanceconstantly have higher precision. The active component of the current isaffected by the line's own resistance and the conductance relative toground, but since both are distributed parameters, the respectiveaccurate measurements are not discussed here. In particular, if theconductance relative to ground has a delta of variation, there can stillbe accurate calculation results when described in terms of lumpedparameters. It can be known that the virtual ground point-to-groundmaintains a residual voltage of 0, and the injection branch can exhibita negative conductance effect, such that accurate LC oscillationconditions are obtained between the equivalent inductance and thecapacitance relative to ground of the injection branch, and thezero-sequence capacitance parameters can be calculated with sufficientaccuracy from the capacitive component of the injection current.

4) Simulation Verification of Single-Phase Being Grounded Via TransitionResistance Based on Virtual Ground Control Method

In particular, phase A is specified as the actual ground point, andR_(k) is grounded at 10Ω, 100Ω, 1000Ω, 10000Ω, or even being notgrounded, such that, following the simulation system described above,the results all reliably converge, i.e., the fault phase-to-groundvoltage converges to 0. Simulation results: FIG. 6 illustrates asimulated fault branch current curve using a system of 10 kV and acompensation current of 150 A, with a single-phase ground faultoccurring in the phase A line at 0.2 second, the ground resistance being10Ω, the control system starting at 0.4 second and basically convergingat about 0.5 second. FIG. 7 illustrates the details of the convergenceprocess.

5) Test Verification of Single-Phase Ground Fault Based on VirtualGround Control Method

Test results: in two resonant ground test systems respectively having aline voltage of 173V and an arc-suppression capacity of 100V5 A/500VAand having a line voltage of 400V and an arc-suppression capacity of230V45 A/10 kVA, the same conclusion is obtained using the virtualground control method. The convergence transition time is 3 to 5 powerfrequency cycles. When calculating according to the nominal value of thecapacitor, the inductive current compensation deviation at resonance isabout 5‰, and the residual voltage reading of the power frequencyvoltmeter is 0V in the case of the single-phase ground, and the controlsystem outputs about 50 mV in real time.

6) Advantages of Virtual Ground Control Method

The virtual ground control method merges problems such as the zeroresidual pressure convergence target, the accurate resonant conditionsetting, the compensation of the active component into one controlsystem in order to form a comprehensive control scheme through properclosed-loop feedback control, so that several problems can be solved atthe same time, whereas the single-phase ground fault, neutral-pointflexible clamp operations, etc. are a set of special cases of virtualground. It is especially important that the measurement of the faultphase (including the virtual fault point)-to-ground voltage belongs to a0-voltage measurement, and the input difference can be 0 using theclosed-loop control of direct residual voltage input. However, in anactual system, the voltage of each phase-to-ground is directly measured,and the zero-detection accuracy of the voltage sensor used is muchhigher than the non-zero measurement accuracy, which is more conduciveto the effective suppression of control deviation and has a bettersuppression effect on the actual residual voltage and the residualcurrent.

7) Using a Scheme for Injecting a Compensation Current with theControlled Source and the Reactance being Parallel

When a partial inductive current is supplied by the existingarc-suppression coil X1, the present disclosure proposes the controlscheme in FIG. 8, where İ_(x1) is a preset reactance current, which canbe a measured current under the action of {dot over (U)}_(GN) and canalso approximately adopt a real-time calculated current under the actionof the fault point voltage {dot over (U)}_(KN) without affecting thesystem convergence.

8) Selection Limitation on Virtual Ground Working Point

As shown in FIG. 9, a Re+jIm phase plane is formed by the three-phasevoltages {dot over (U)}_(a), {dot over (U)}_(b), {dot over (U)}_(c), andone phasor circle ABC is formed by the three voltage phasors having aradius with an effective value being 5775V. When the device insulationis not counted, the point K can be arbitrarily selected in the phaseplane, and the K point is equivalently grounded by the virtual groundmethod. The distribution system has physical ground points only when A,B, C, and N are selected: any phase bus of A, B, and C, or a neutralpoint N.

When used as a measurement in the above 3), a small phasor circle, suchas the 100V phasor circle in FIG. 9, can be set, and the preset phasor{dot over (U)}_(KN) is defined on the circle, such that a zero-sequenceresonance measurement with an effective value of 100V can be performed.After convergence of the point K-to-ground, the offset of the threephases relative to ground is not large, which does not affect the normaloperation of the system. The point K1 in FIG. 9 is the same phasevoltage of A, and the effective value is 100V. In actual use, measuringthe magnitude of the effective value can be adjusted as needed, and theinjection capacity satisfies the U²/Z relationship and contains a smallproportion of the active component.

When considering insulation safety, if the effective value of eachphase-to-ground voltage does not exceed √{square root over (3)}U_(φ), acircular arc having a radius with the effective value of √{square rootover (3)}U_(φ) can be formed by respectively taking A, B, and C as thecenter, and the three circular arcs close an area. Setting the workingpoint K in this area can achieve that the limit of the insulationvoltage of each phase-to-ground is not broken. If it is necessary todetect the insulation tolerance of the phase A, the phase voltagedirection opposite to the phase A can be selected. For example, whensetting according to the K2 direction in FIG. 9, the phase A-to-groundvoltage can appropriately increase, and the voltages of the phases B andC relative to ground will decrease, so that the insulation tolerance ofthe phase A can be tested.

When further considering the phase-to-ground safety voltage, if it issupposed that the phase B-to-ground insulation is damaged but the faultyrunning time still needs to be extended, the target working point K3 canbe selected in this area and near the point B and the withstand voltageof phase B relative to ground is appropriately reduced according to theactual insulation tolerance, and even operating by being grounded.However, the voltages of phases A and C relative to ground will increasecorrespondingly and will not break the insulation voltage limit.

8) Description of the Implementation of Virtual Ground Control Method

The control scheme proposed by the present disclosure is a scheme inwhich a controlled voltage source is injected into a system neutralpoint via reactance, which, in essence, is a current injection behavior.The connection reactance L has a certain leveling effect on the systemvoltage disturbance and the controlled source voltage disturbance, whichis superior to the rigid voltage clamping manner. In the injectionmanner, the injection can be performed in a direct-hanging mode in whichthe compensation current is directly injected into the neutral point,and it is also possible to use an isolation transformer to inject acompensation current into the neutral point. Whether or not an isolationtransformer is used has no essential impact on this control scheme.

When there is a potential oscillation overvoltage factor in the system,point N clamping can be considered, or a limited offset voltage isapplied, so as to make the system operate stably in a low-voltageresonant clamping state, which helps to suppress system oscillation.

The theoretical basis on which the present disclosure relies isreliable, and the control method is very simple, which expands theexisting zero-sequence measurement and arc-suppression theory, hasexcellent performance in many aspects such as measurement, accurateresonance control, residual pressure suppression and the like, can befurther broadened to applications such as insulation exploration withoutproviding the measurement part, and thus is a unified control schemewith universal applicability. Both simulation and experimentation showthat when there is a certain degree of asymmetry in the powerdistribution network, the system can still work stably. This is an idealmeasurement and control scheme for the single-phase ground fault inresonant ground systems.

Similar control schemes obviously constructed by the scheme proposed bythe present disclosure, whose fundamental properties have not changedsignificantly, are also within the scope of the present disclosure.

What is claimed is:
 1. A zero-sequence parameter measurement and groundvoltage control method for a resonant ground system based on a virtualground principle, the method comprising: arbitrarily specifying a pointK in a phasor plane in which three-phase voltages are located, a voltagerelative to a neutral point N being {dot over (U)}_(KN); using a groundpoint voltage zeroing control approach to achieve virtual ground of thepoint K, and obtaining an accurate zero-sequence resonant parameter of azero-sequence network under an action of excitation of {dot over(U)}_(KN); specifying a ground phase as a target working point when afault phase is grounded; and applying the above ground point voltagezeroing control approach to cause the zero-sequence network toaccurately resonate, a voltage of the phase relative to ground being 0,and at this time, both a residual voltage and a residual current of thefault phase are effectively suppressed.
 2. The zero-sequence parametermeasurement and ground voltage control method for a resonant groundsystem based on a virtual ground principle according to claim 1, whereinthe ground point voltage zeroing control approach is as follows: using aconventional resonant ground mariner, the neutral point N being groundedvia a series branch of an arc-suppression inductance L, an equivalentresistance R and a controllable inverter source unit {dot over (U)}_(x),an injection current of the branch being İ_(x); and taking a fractionL₀/m of a standard arc-suppression reactance L₀ as an injection branchreactance L, L₀ and C₀ satisfying a resonant condition: ω²L₀C₀ = 1then:${\overset{.}{U}}_{x} = {{\left( {1 - \frac{1}{m}} \right){\overset{.}{U}}_{KN}} + {j\; \omega \; C_{0}R{\overset{.}{U}}_{KN}} + {\left( {R + {j\; \omega \; L}} \right)Y_{0}{\overset{.}{U}}_{KN}}}$wherein {dot over (U)}_(KN) is a voltage of the specified point Krelative to the neutral point N, C₀ is a total zero-sequence capacitanceand is a sum of a distributed capacitance of three phases, Y₀ is a totalzero-sequence conductance and is a sum of a distributed conductance ofthe three phases, and ω is a power frequency angular frequency of apower distribution network; taking a virtual working point K-to-groundvoltage {dot over (U)}_(KG) as an input and taking a ground-to-neutralpoint N voltage {dot over (U)}_(GN) and a voltage drop of the systemzero-sequence network current on the injection branch as corrections toconstruct a negative feedback control loop, taking an appropriatecomplex phasor proportional integral parameter cPI[K_(p)+K_(i)/s], andcausing the zero-sequence circuit to enter into an LC parallel resonantstate, a loop circuit input U_(KG) converging to 0, PI controlcalculation being applied to both a real part and an imaginary part ofan input complex phasor, a governing equation being as follows:{dot over (U)} _({tilde over (x)}) ={dot over (U)} _(GN)+(R+jωL)(İ _(C0)+İ _(Y0))+cPI[{dot over (U)} _(KG)(R+jωL)/R _(k)] wherein a complexphasor proportional integral part is:cPI[a+jb]=a(Kp+Ki/s)+jb(Kp+Ki/s) where R_(K) is a virtual workingpoint-to-ground transition resistance, and İ_(C0)+İ_(Y0) is a linezero-sequence total current and is a complex constant under a resonanceconvergence condition.
 3. The zero-sequence parameter measurement andground voltage control method for a resonant ground system based on avirtual ground principle according to claim 2, wherein two parameters ofthe line zero-sequence total current İ_(C0)+İ_(Y0) and an impedanceR_(k) are ignored, and the governing equation is simplified as:{dot over (U)} _({tilde over (x)}) =cPI[{dot over (U)} _(KG)].
 4. Thezero-sequence parameter measurement and ground voltage control methodfor a resonant ground system based on a virtual ground principleaccording to claim 2, wherein in the method, when a controlled voltagesource is injected into the neutral point of the system via thereactance, the injection can be performed in a direct-hanging mode,i.e., a compensation inductive current is injected directly into theneutral point, or a compensation current is injected into the neutralpoint by using an isolation transformer.
 5. The zero-sequence parametermeasurement and ground voltage control method for a resonant groundsystem based on a virtual ground principle according to claim 2, whereina phase plane is formed by the three-phase voltages {dot over (U)}_(a),{dot over (U)}_(b), {dot over (U)}_(c), and one phasor circle ABC isformed by three voltage phasors, and a selection principle of the pointK is as follows: 1) when considering device insulation, selecting anarbitrary point in the phase plane formed by the three-phase voltages{dot over (U)}_(a), {dot over (U)}_(b), {dot over (U)}_(c), as the pointK; 2) when performing zero-sequence parameter measurement, selecting aphasor circle in the phase plane with an effective value of the measuredvoltage being a radius, and point K being limited on the phasor circle;3) when considering insulation safety, if an effective value of eachphase-to-ground voltage does not exceed √{square root over (3)}U_(φ),forming a circular arc having a radius with an effective value of√{square root over (3)}U_(φ) by taking A, B, and C as a centerrespectively, three circular arcs closing an area, selecting the workingpoint K in this area; and 4) considering a phase-to-ground safetyvoltage, if it is supposed that phase B-to-ground insulation is damagedbut a faulty running time still needs to be extended, selecting thetarget working point K in the area of 3) and near the point B, andappropriately reducing a withstand voltage of phase B relative to groundaccording to an actual insulation tolerance.